Educational device for use in conversion between number systems

ABSTRACT

An educational device comprising a base member, a front panel having a plurality of windows, arranged in rows and columns movable indicator members viewable through the windows to provide numeric information useful in the conversion between number systems. In one embodiment the movable indicator members include a slide member and a plurality of rotatable discs. In a second embodiment the movable indicator members comprises a plurality of rotatable drums.

United States Patent In ventor Arthur Moskowltz Winter Park, Fla. Appl.No 18,839 Filed Apr. 15, 1970 Patented Aug. 17, 1971 Assignee The UnitedStates 0! America as repraented by the Secretary of the Navy EDUCATIONALDEVICE FOR USE [N CONVERSION BETWEEN NUMBER SYSTEMS [56] ReferencesCited UNITED STATES PATENTS 1,246,860 11/1917 Brachtl et a1. 35/76 UX1,394,305 10/1921 Hurley... 35/76 3,055,121 9/1962 Neal 35/31 A PrimaryExaminer-William H. Grieb Attorneys-Richard S. Sciascia, John W. Peaseand Harvey A.

David ABSTRACT: An educational device comprising a base member, a frontpanel having a plurality of windows, arranged in rows and columnsmovable indicator members viewable 9 Claim" 14 Drawing Figs through thewindows to provide numeric information useful in US. Cl 35/30 theconversion between number systems. In one embodiment Int. Cl ...G09b19/02 the movable indicator members include a slide member and a Fieldof Search 35/30, 31 plurality of rotatable discs. ln a second embodimentthe mova- R, 31 A,74, 76; 235/71, 74, 85,86,88. I08, 114, ble indicatormembers comprises a plurality of rotatable 125 drums.

P os Uflfl fi l '1 w 32 g g 2 45 6 9 J L BA s5 2 jg JJ 9 j a 1v. 2 3/5'6 j E I 2 0 o 3--- 0 1 1 L a A s E 3 a-- a 9 e E e o o o 0 c I L BA 5 E4 M... m E9 E7 E7 E E i O O O O 3 a A s E 1% POSITION WEIG'H IEDUCATIONAL DEVICE FOR USE IN CONVERSION BETWEEN NUMBER SYSTEMSSTATEMENT OF GOVERNMENT INTEREST The invention described herein may bemanufactured and used by or for the Government of the United States ofAmerica for governmental purposes without royalties thereon or therefor.1

BACKGROUND OF THE INVENTION This invention relates to educationaldevices and more particularly to devices useful in the teaching andunderstanding of different number systems and the principles ofconversion from one number system to another.

With increased use of digital computers by the Armed Services andindustry, additional courses of instruction are being given by militaryand public schools alike in the fundamentalsof digital computation. Oneof the difficulties encountered in the teaching and learning of digitalcomputation is that concerned with number systems different from the onewe normally use, i.e. the decimal or base system. Decimal numbers areinstantly recognized and read,or calculations performed with them,either on paper or in our heads, without considering all the arithmeticprocesses involved. However, to properly-understand the basic operationof digital computers, it is necessary to analyze number systems and tobreak down each arithmetic process to its simplest parts.

SUMMARY OF THE INVENTION With the foregoing in mind, it is a principalobject of this invention to provide a number systems calculating andinstructional device for use by computer operators and techniciansrequiring a knowledge of computer mathematics in order to understand theoperation of and perform maintenance on computer equipment.

It is another object of the invention to provide an improved device ofthe foregoing character which will fulfill an existing need in'schoolsteaching digital computer fundamentals or the topic of number system inmathematics courses, and which will be useful to engineers, dataprocessing and programming personnel in providing them with readyreference for converting between number systems.

As another object the invention aims to provide a convenient, hand-heldcalculator and instructional device useful in converting a numberexpressed in any base number system (from base 2 to base 9) to itsdecimal equivalent, or vice versa, and useful in converting any givennumber in a system to an equivalent number in any other system from base2 to base 9.

Still another object of the invention is the provision of such a devicewhich can be economically manufactured of plastics or the like and canbe supplied to students as a hand-out item which can be retained bythem.

The invention may be further said to reside in certain novelconstructions, combinations, and arrangements of parts by which theforegoing objects and advantages are achieved, as well as others whichwill become apparent from the following detailed description of thepreferred embodiments when read in conjunction with the accompanyingsheets of drawings.

DESCRIPTION OF THE DRAWINGS tion with some portions broken away and insection;

FIG. 9 is an end view of the device of FIG. 8; FIG. 10 is a side view ofthe device of FIG. 8 with other'portions broken away;

the payment of any FIG. 11 is a fragmentary view, on an'enlarged scale,showing details of construction of the device of FIG. 8;

FIG. 12 is a sectional view taken substantially along line 12-12 ofFIG.11; l s

FIG. 13 is a sectional view taken substantially along line 13-13 ofFIG.1l;and i I FIG. 14 is a perspective view of an indicator drum of thedevice of FIG. 8Q

DESCRIPTION OF THE PREFERRED EMBODIMENTS In the form of the inventionillustrated in FIGS. 1 through 7 of the drawings, and describedhereinafter, there is provided a number system converting device,generally indicated at 10.

I The device 10 comprises generally flat, rectangular base member 12which is conveniently formed, as by molding, of a suitable plasticmaterial such as polyvinylchloride. The base member 12 carries, eitherintegrally therewith or cemented thereto, spacing means including aplurality of posts 14, ribs l6, 18, 20, and 22, and a thickened cornerarea 24. I

Mounted on the spacer means l4, l6, 18, 20, 22, and 24 is a generallyrectangular front panel 26, also conveniently molded of plastic and heldin spaced, congruent relation to the base member by cement or the likeapplied between the front panel and the spacer meansyThe front panel 26is characterized by a plurality of windows 30 arranged, as viewed inFIG/1, in eight horizontal rows of five windows in each row. Each row isutilized with reference to an individual number system. Thus, the toprow, as viewed in FIG. 1, has reference to the number system having asbase of 2, the next row has reference to the number system having a baseof 3, and so on to the last row which has reference to the number systemhaving a base of 9. Moreover, the windows 30 are arranged in verticalcolumns representing positions in a number. Thus, the right-hand columnis designated position 0, the next column to the left as position I, andso on to the last column on the left which is designated as position 4.Adjacent each window 30 is an opening 32, the purposes of which windowsand openings will become apparent as this description proceeds.

Disposed between the base member 12 and the front panel 26 are aplurality of rotatable indicia-carrying elements in the form of discs34. Referring to FIGS. 6 and 7 which illustrate a representative one ofthe discs 34, it will be seen that these discs are each provided with anaxially extending knob 36. The knobs are rotatably received through theopenings 32 in the front panel 26. Each of the discs 34 carry inner andouter sets of numerals which are circularly arranged so that selectednumbers comprised of those numerals appear in the windows 30 uponrotation of the knobs 36.

Reverting to FIG. 1, it will be seen that between the front panel 26 andthe base member 12 the spacer ribs l6, l8, and 20, and the thickenedcorner area 24 define a rectangular cavity 40. In this space 40 isdisposed a movable, rectangular slide member 42, the long dimension ofwhich is substantially shorter than the long dimension of the cavity 40.The slide member 42, which is best illustrated in FIG. 5, is providedwith a knob 44 which extends through a slot 46 defined in the frontpanel 26. The slide member 42 carries rows of numbers in two sets thefirst of which are selectively viewable through windows 50 and $2 in thefront panel 26, and the second of which sets are selectively viewablethrough windows 54, 56, 58, 60, and 62 in the front panel uponmovementof the slide through the agency of the knob 44. Operation of theslide 42 to bring to view in window 50 a base number ofa system to beinvolved in a conversion will bring into view in window 52 the usablenumbers in that system, and will also bring into view in windows 54, 56,$8, 60, and 62 numbers which are the decimal weight factor to be appliedto the usable numbers when located in the positions 4, 3, 2, l. andrepresented respectively by the last mentioned windows. Thus, if theslide 42 is positioned as illustrated in FIG. 1 with the base number ofradix 3 appearing in window 50, it will be seen that the usable 5numbers for the base 3 system are 0, l, and 2. 1t will also be seen fromwindows 54-62 that the weight factor for position 4 is 8 l for position3 is 27, for 2 is 9, for l is 3, and for 0 is 1.

Now, the inner circle of numbers on each disc 34 represents 10 theusable numbers for the base system for which the particular disc is tobe used. Thus, each disc in the second row (base 3) will have as itsinner circle of numbers, those numbers showing in the window 52.Similarly, the typical disc illustrated in FIG. 6 has as its innercircle of numbers the usable numbers for base 8.

The outer circle of numbers on each disc 34 comprises, corresponding toeach inner circle number, the product of that inner circle number andthe position weight factor for the base number and the position numberfor which the particular disc is to be used. The following tables willprovide the corresponding inner and outer numbers for each of the fortydiscs 34 used in the device 10:

BASE 2 Outer circle numbers in place positions Inner circle numbers: 0 0l) 0 0 0 1,. 16 8 4 2 1 BASE 3 Outer circle numbers in place positionsInner circle numbers:

BASE 4 5 Outer circle numbers in place positions Inner circle numbers:

BASE 5 55 Outer circle numbers in place positions Inner circle numbers:

BASE 6 Outer circle numbers in place positions BASE 7 O uter circlenumbers in place positions Inner circle numbers:

BASE 8 Outer circle numbers in place positions Inner circle numbers:

BASE 9 Outer circle numbers in place positions Inner circle numbers Inthe operation of the device 10, if it is desired to convert the ternaryor base 3 number 2102 to its decimal equivalent, it is first necessaryto turn the knobs 36 in the base 3 row so that the ternary number isrepresented by the inner circle numbers appearing in the windows 30 asis illustrated in FIG. 1. l'hus, the position 3 knob is rotated to showthe inner circle number 2 and its corresponding outer circle number 54,the position 2 knob is rotated to show the inner circle number and thecorresponding outer circle number 9, the position 1 knob is rotated toshow inner and outer numbers 0 and 0, and the position 1 knob to shownumbers 2 and 2. Now, the outer circle numbers are merely added,rendering the decimal number 65 as the equivalent of the ternary number2102.

Supposing one desires to convert a decimal number eg. 3389 to its octalor base 8 equivalent, it is first necessary to operate the slide knob 44to bring numeral 8 into view in window 50, This will place in the window52 the usable numbers enclosed in the dotted line representation ofwindow 52 in FIG. 5. This will also place in windows 54, 56, 58, 60 and62 the position weight numbers as shown in FIG. 5, which numbers arepowers of 8 Next, find the largest position weight number (power of 8)in 3,389. The position 4 weight number 4,096 is too large, but theposition 3 weight number 512 will go. Accordingly, the position 3 knobin the base 8 row is rotated to bring the largest outer number into viewwhich will go into 3,389. This is seen to be the number 3,072 which hasa corresponding inner number of 6. The difference between 3,389 and3,072 is 317. Accordingly the position 2 knob is rotated to show thelargest outer number which will go into 3 l 7, namely 256, thecorresponding inner number being 4.

The difference between 317 and 256 is 61, so the position 1 knob isturned to bring into view the largest number which will go into 61,namely 56, the corresponding inner number being 7. The differencebetween 61 and 56 is 5, so the zero position knob is rotated to bringouter number 5 into view with its corresponding inner number 5. Theoctal number 6,475 is now To change from a number of a first nondecimalbase to a number 'of a second nondecimal base it is only necessary toconvert the number from the first nondecimal base into decimal form as amiddle step and then from decimal form into thesecond hondecimal baseusing the same principles as exemplified above.

Another embodiment of the invention, indicated generallly at 90, willbedescribed with reference to FIGS. 8-14. The device 90 comprises arectangular boxlike base member 92 which is divided lengthwise byparallel wall portions 92a into five cavities. A front panel 94 ismounted on the base member 92 and is provided with a plurality ofwindows 96 arranged in eight horizontal rows of five windows in eachrow, the windows being also arranged in five vertical columns. As in thedevice 10, each of the eight rows is representative of a number ofsystem from base 2 to base 9, and the columns are. representative ofposition places in the number systems.

Additional windows 98 and 100 are provided for revealing, respectively,a selected base number and the usable numbers in the selected system.Windows 102, 104, 106 and 108, and 110 are provided toreveal theposition weights corresponding to a selected number system.

Mounted in the base 92 for viewing through the windows 96 are aplurality of indicator drums 114. The drums 1 14, which are separated bythe wall portions 92a, are rotatably mounted on axle shafts 116extending through apertures in the wall portions and secured as bycementing Each drum 114, best illustrated in FIG. l4, comprises a raisedthumbwheel 114a, the periphery of which extends above the surface of thefront paneL-as shown in FIG. 13, to permit easy rotation of the drum.The thumbwheel also serves to divide the drum into left and rightsegments on which are placed numbers which are equivalent to the numbersin the inner and outer circles, respectively, of the discs 34 of thedevice 10. I

As is best illustrated in FIGS. 11 and 12, the device 90 com prisesindicator drums 118 and 120, the drum 118 bearing numbers which are tobe displayed through windows 98, 100, and the drum 120 bearing numberswhich are to be displayed through windows 102, 104, 106, 108, and 110.The drum 118 has thumbwheels 122 for manipulation thereof, the drumbeing fixed to a shaft 124 which is journaled in apertures in the wallportions of the base member 92. Fixed to the shaft 124 for rotationtherewith is a pinion gear 126 which is in driving mesh with an idlergear 130 which is in turn in driving mesh with a gear 132 fixed to thedrum 120. The latter is rotatably supported by a shaft 134. Operation ofa thumbwheel 122 to bring a selected base number into view in window 98will simultaneously bring the usable numbers of the selected system intoview in window 100, and, through the operation of gears 126, 130 and132, will bring the appropriate position weight numbers into view in thewindows 102, 104, 106, 108, and 1 10.

In order to preclude undesired rotation of the drums 114 from selectedpositions, a spring washer 136 is conveniently inserted between eachdrum 114 and an adjacent wall portion of the base 92.

Similarly an identical washer 136 is disposed between the drum 120 andthe adjacent wall portion of the base 92. The latter washer serves tomaintain the positions of both of drums 1 18 and 120 inasmuch as theyare geared together. I

It will be appreciated that the drums 118, 120 and the associatedgearing provide the same information as the slide 42 in the earlierdescribed device 10. Operation of the device 92 is generally the same asthat of the device 10, remembering that the numbers on the left andright portions of the drums 114, viewable through the windows 96,correspond respectively to the inner and outer circles of numbers on thediscs 34. Accordingly, no further description of the operation of thedevice 92 is believed necessary.

Fran the f rssa nss e l ss er pfi asfset ralsm qd r ments of theinvention it will be recognized that the aforementioned objects andadvantages have been achieved, as well as others apparent from thedescription. V

Obviously many modifications and variations of the present invention arepossible in the light of the above teachings. It is therefore to beunderstood that-within the scope of the appended claims the inventionmay be practiced otherwise than as specifically described.

What I claim is:

1. A device for use in conversion of numbers from a number system of onebase to a number system of a different .base, said device comprising:

a rectangular base having a plurality of rotatable indicator meansarranged in horizontal rows and vertical columns, each row correspondingto a different number system and the number of indicator means in-eachrow corresponding to the number of number numbers to be accommodated foreach number system;

each of said indicator means in any given row having first and secondsets of numbers thereon, the first set representing usable numbers forthe system of the given row and the second set comprising the productsof the usable number and position weight'values for the respectivenumber position columns occupied by the indicator means;

panel means overlying said base and said indicator means,

said panel means having a plurality of windows corresponding to saidplurality of indicator means; and

manual operating means connected to each of said indicator means foreffecting selected movements thereof to bring selected ones of saidfirst and second sets of numbers into view through said windows.

2. A-device as defined in claim 1, and further comprising:

additional indicator means mounted on' said base member and beneath saidpanel means;

said panel means having additional windows therein; and means foractuating said additional indicator means to simultaneously bring intoview in said additional window means a selected system base number andthe usable numbers for the selected system.

3. A device as defined in claim 1, and wherein:

said indicator means each comprises a disc; and

said manual operating means comprises a knob extending upwardly fromeach disc through said panel means.

4. A device as defined in claim 2, and wherein:

said additional indicator means comprises a rectangular slide member; e

said base member and said panel means defining a space I wherein saidslide and a knob extending from said slide through a slot in said panelmeans for effecting linear movement of said slide. 5. A device asdefined in claim 3, and further comprising: additional indicator meansmounted on said base member and beneath said panel means; said panelmeans having additional windows therein; means for actuating saidadditional indicator means to simultaneously bring into view in saidadditional window means a selected system base number and the usablenumbers for the selected system; said additional indicator meanscomprising a rectangular slide member; i said base member and said panelmeans defining a space wherein said slide can be moved linearlytherebetween; and a knob extending from said slide through a slot insaid panel mea n s fgr etjfec ting linear movement of said slide.

6. A device as defined in claim 1, and wherein: i said indicator meanseach comprises a drum rotatably supported with respect to said base;said manual operating means comprises a thumbwheel extending radiallyfrom each of said drums, with the periphery of said thumbwheel extendingabove the upper surface of said panel means; and said thumbwheel servingto diyide the associated drum into can be moved linearly therebetween;

two separate indicator surfaces for said first and second sets ofnumbers, respectively.

7. A device as defined in claim 6, and further comprising: additionalindicator means mounted on said base member and beneath said panelmeans;

said panel means having additional windows therein; and

means for actuating said additional indicator means to simultaneouslybring into view in said additional window means a selected system basenumber and the usable numbers for the selected system.

87 A device as defined in claim 7, and wherein said additional indicatormeans comprises:

a first additional drum rotatably mounted on said base and having athumbwheel for rotation thereof;

1!. sssqngsitieaatsizsm rqta ah ys p sme 91!. a dsbas for-rotation aboutan axisparallel to that of said first additional drum;

a driving gear connected to said first additional drum for rotationtherewith;

an idler gear rotatably mounted on said base and in mesh with saiddriving gear; and

a driven gear connected to said second additional drum and in mesh withsaid idler gear, so that rotation of said first additional drum by thethumbwheel thereof will effect simultaneous rotation of said secondadditional drum.

9. A device as defined in claim 8 and further comprising:

resilient means disposed between the first mentioned drums and said basefor frictionally resisting rotation of said drums.

1. A device for use in conversion of numbers from a number system of one base to a number system of a different base, said device comprising: a rectangular base having a plurality of rotatable indicator means arranged in horizontal rows and vertical columns, each row corresponding to a different number system and the number of indicator means in each row corresponding to the number of number numbers to be accommodated for each number system; each of said indicator means in any given row having first and second sets of numbers thereon, the first set representing usable numbers for the system of the given row and the second set comprising the products of the usable number and position weight values for the respective number position columns occupied by the indicator means; panel means overlying said base and said indicator means, said panel means having a plurality of windows corresponding to said plurality of indicator means; and manual operating means connected to each of said indicator means for effecting selected movements thereof to bring selected ones of said first and second sets of numbers into view through said windows.
 2. A device as defined in claim 1, and further comprising: additional indicator means mounted on said base member and beneath said panel means; said panel means having additional windows therein; and means for actuating said additional indicator means to simultaneously bring into view in said additional window means a selected system base number and the usable numbers for the selected system.
 3. A device as defined in claim 1, and wherein: said indicator means each comprises a disc; and said manual operating means comprises a knob extending upwardly from each disc through said panel means.
 4. A device as defined in claim 2, and wherein: said additional indicator means comprises a rectangular slide member; said base member and said panel means defining a space wherein said slide can be moved linearly therebetween; and a knob extending from said slide through a slot in said panel means for effecting linear movement of said slide.
 5. A device as defined in claim 3, and further comprising: additional indicator means mounted on said base member and beneath said panel means; said panel means having additional windows therein; means for actuating said additional indicator means to simultaneously bring into view in said additional window means a selected system base number and the usable numbers for the selected system; said additional indicator means comprising a rectangular slide member; said base member and said panel means defining a space wherein said slide can be moved linearly therebetween; and a knoB extending from said slide through a slot in said panel means for effecting linear movement of said slide.
 6. A device as defined in claim 1, and wherein: said indicator means each comprises a drum rotatably supported with respect to said base; said manual operating means comprises a thumbwheel extending radially from each of said drums, with the periphery of said thumbwheel extending above the upper surface of said panel means; and said thumbwheel serving to divide the associated drum into two separate indicator surfaces for said first and second sets of numbers, respectively.
 7. A device as defined in claim 6, and further comprising: additional indicator means mounted on said base member and beneath said panel means; said panel means having additional windows therein; and means for actuating said additional indicator means to simultaneously bring into view in said additional window means a selected system base number and the usable numbers for the selected system.
 8. A device as defined in claim 7, and wherein said additional indicator means comprises: a first additional drum rotatably mounted on said base and having a thumbwheel for rotation thereof; a second additional drum rotatably mounted on said base for rotation about an axis parallel to that of said first additional drum; a driving gear connected to said first additional drum for rotation therewith; an idler gear rotatably mounted on said base and in mesh with said driving gear; and a driven gear connected to said second additional drum and in mesh with said idler gear, so that rotation of said first additional drum by the thumbwheel thereof will effect simultaneous rotation of said second additional drum.
 9. A device as defined in claim 8 and further comprising: resilient means disposed between the first mentioned drums and said base for frictionally resisting rotation of said drums. 